The answer to every question is, "It depends". Our entertainment systems are likely similar so I will describe how mine works. Hopefully you can glean something from that.
Caveat. All the OEM components, save the speakers, in my system have been replaced with new, hopefully better.
The amplifier for the original system, and present, is integral to our (Sony) Home Entertainment 5.1 system. As it was to the OEM.
The dash radio is a 5.1 JVC. All the speaker wires input to a "six channel speaker switch with crossover" (mfg description). This device is located near the Sony. All the Sony speaker wires input to the speaker switch also. The switch output leads to all the various speakers in the system. In our case, two right, two left, one center and two woofers. That is a gazillion speaker wires. Luckily, Winnebago printed each wire with their ID.
If you are missing the six channel switch (original about 9 x 6 x 2in, new about 4 x 3 x 1) call Riverpark, 21953 Protecta Dr. Elkhart, IN 574-522-7781
There is a rocker switch near Sony (which I moved to beneath the TV) labeled Radio and DVD. That tells the six channel switch which input to send to the speakers.
Finally to your specific question.
You need to have a TV that has audio output (either RCA or HDMI) and you have to have a home entertainment unit that will accept that audio output. Probably, your home entertainment unit (my Sony) will default to the DVD for sound. You likely have to tell it to play TV, Aux or whatever. They are all a little bit different.
In summary, I rocker the switch to radio for radio, rocker it to DVD for DVD or TV. The TV plays only after I have directed the Sony to accept TV for play thru.
Hope that is helpful.
Fair Winds and Following Seas